Rank four temperaments

441/440

Commas 441/440, 364/363

13-limit minimax
[|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>,
|1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>,
|1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]
Eigenmonzos: 2, 11/10, 8/7, 16/13

15-limit minimax
[|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>,
|5/4 -3/4 5/4 -1/4 -1/4 1/4>,
|17/8 -11/8 5/8 -1/8 3/8 1/8>,
|5/2 -3/2 1/2 -1/2 1/2 1/2>,
|17/8 -11/8 5/8 -9/8 3/8 9/8>]
Eigenmonzos: 2, 14/13, 6/5, 11/9

Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657
Map to lattice: [<0 1 1 -1 -1 0|,
<0 0 1 0 -1 -2|, <0 0 1 1 1 1|]

Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|,
<0 0 1 0 -1 -2|, <0 0 0 1 2 3|]
Generators: 2, 3, 5
Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393

Commas 441/440, 351/350

385/384

Commas 385/384, 325/324

13 and 15 limit minimax
[<1 0 0 0 0 0|, <0 1 0 0 0 0|,
<2/3 4/3 1/3 0 0 -1/3|,
<19/6 -1/6 -1/6 1/2 -1/2 1/6|,
<19/6 -1/6 -1/6 -1/2 1/2 1/6|,
<2/3 4/3 -2/3 0 0 2/3|]
Eigenmonzos: 2, 14/11, 13/10, 4/3

Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247

Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|,
<0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]
Generators: 2, 3, 5, 7
Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253

9801/9800

Commas 2080/2079, 1716/1715

13 and 15 limit minimax
[|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>,
|7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>,
|11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]
Eigenmonzos: 2, 6/5, 16/13, 9/7

Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299

Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|,
<0 0 1 0 1 0|, <0 0 0 1 1 2|]
Generators: 99/70, 3, 5, 7
Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892